Phase transitions for the long-time behaviour of interacting diffusions

@inproceedings{Greven2008PhaseTF,
  title={Phase transitions for the long-time behaviour of interacting diffusions},
  author={Andreas Greven and F. den Hollander},
  year={2008}
}
Let ({Xi(t)}i∈Zd)t≥0 be the system of interacting diffusions on [0,∞) defined by the following collection of coupled stochastic differential equations: dXi(t) = ∑ j∈Z a(i, j)[Xj(t) − Xi(t)] dt + √ bXi(t) dWi(t), i ∈ Z, t ≥ 0. Here, a(·, ·) is an irreducible random walk transition kernel on Z ×Zd, b ∈ (0,∞) is a diffusion parameter, and ({Wi(t)}i∈Zd)t≥0 is a collection of independent standard Brownian motions on R. The initial condition is chosen such that {Xi(0)}i∈Zd is a shift-invariant and… CONTINUE READING